Dual Nature Of Radiation And Matter Ques 10
10. A particle of mass $1$ $ mg$ has the same wavelength as an electron moving with a velocity of $3 \times 10^{6}$ $ms^{-1}$. The velocity of the particle is:
[2008]
(a) $2.7 \times 10^{-18} $ $ms^{-1}$
(b) $9 \times 10^{-2} $ $ms^{-1}$
(c) $3 \times 10^{-31} $ $ms^{-1}$
(d) $2.7 \times 10^{-21} $ $ms^{-1}$
(mass of electron $=9.1 \times 10^{-31} kg$ )
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Answer:
Correct Answer: 10.(a)
Solution:
- (a) Wavelength of particle
$ (\lambda_1)=\frac{h}{mv}=\frac{h}{(1 \times 10^{-6}) \times v} $
where $v$ is the velocity of the particle.
Wave length of electron,
$ (\lambda_2)=\frac{h}{(9.1 \times 10^{-31}) \times(3 \times 10^{6})} $
But $\lambda_1=\lambda_2$ (Given)
$ \begin{aligned} & \therefore \frac{h}{(1 \times 10^{-6}) \times v}=\frac{h}{(9.1 \times 10^{-31}) \times(3 \times 10^{6})} \\ & \Rightarrow v=\frac{9.1 \times 10^{-31} \times 3 \times 10^{6}}{10^{-6}}=2.73 \times 10^{-18} ms^{-1} \end{aligned} $
BETA
